Merge branch 'master' into master

mathgenerator/mathgen.py

@@ -280,10 +280,55 @@ def thirdAngleOfTriangleFunc(maxAngle=89):
 	angle1 = random.randint(1, maxAngle)
 	angle2 = random.randint(1, maxAngle)
 	angle3 = 180 - (angle1 + angle2)
-	problem = "Third angle of triangle = "
+	problem = f"Third angle of triangle with angles {angle1} and {angle2} = "
 	solution = angle3
 	return problem, solution
 
+def systemOfEquationsFunc(range_x = 10, range_y = 10, coeff_mult_range=10):
+    # Generate solution point first
+    x = random.randint(-range_x, range_x)
+    y = random.randint(-range_y, range_y)
+    # Start from reduced echelon form (coeffs 1)
+    c1 = [1, 0, x]
+    c2 = [0, 1, y]
+
+    def randNonZero():
+        return random.choice([i for i in range(-coeff_mult_range, coeff_mult_range)
+                              if i != 0])
+    # Add random (non-zero) multiple of equations (rows) to each other
+    c1_mult = randNonZero()
+    c2_mult = randNonZero()
+    new_c1 = [c1[i] + c1_mult * c2[i] for i in range(len(c1))]
+    new_c2 = [c2[i] + c2_mult * c1[i] for i in range(len(c2))]
+
+    # For extra randomness, now add random (non-zero) multiples of original rows
+    # to themselves
+    c1_mult = randNonZero()
+    c2_mult = randNonZero()
+    new_c1 = [new_c1[i] + c1_mult * c1[i] for i in range(len(c1))]
+    new_c2 = [new_c2[i] + c2_mult * c2[i] for i in range(len(c2))]
+
+    def coeffToFuncString(coeffs):
+        # lots of edge cases for perfect formatting!
+        x_sign = '-' if coeffs[0] < 0 else ''
+        # No redundant 1s
+        x_coeff = str(abs(coeffs[0])) if abs(coeffs[0]) != 1 else ''
+        # If x coeff is 0, dont include x
+        x_str = f'{x_sign}{x_coeff}x' if coeffs[0] != 0 else ''
+        # if x isn't included and y is positive, dont include operator
+        op = ' - ' if coeffs[1] < 0 else (' + ' if x_str != '' else '')
+        # No redundant 1s
+        y_coeff = abs(coeffs[1]) if abs(coeffs[1]) != 1 else ''
+        # Don't include if 0, unless x is also 0 (probably never happens)
+        y_str = f'{y_coeff}y' if coeffs[1] != 0 else ('' if x_str != '' else '0')
+        return f'{x_str}{op}{y_str} = {coeffs[2]}'
+
+    problem = f"{coeffToFuncString(new_c1)}, {coeffToFuncString(new_c2)}"
+    solution = f"x = {x}, y = {y}"
+    return problem, solution
+
+    # Add random (non-zero) multiple of equations to each other
+
 # || Class Instances
 
 #Format is:
@@ -311,3 +356,5 @@ doesTriangleExist = Generator("Triangle exists check", 19, "Does triangle with s
 midPointOfTwoPoint=Generator("Midpoint of the two point", 20,"((X1,Y1),(X2,Y2))=","((X1+X2)/2,(Y1+Y2)/2)",MidPointOfTwoPointFunc)
 factoring = Generator("Subtraction", 21, "x^2+(x1+x2)+x1*x2", "(x-x1)(x-x2)", factoringFunc)
 thirdAngleOfTriangle = Generator("Third Angle of Triangle", 22, "Third Angle of the triangle = ", "angle3", thirdAngleOfTriangleFunc)
+systemOfEquations = Generator("Solve a System of Equations in R^2", 23, "2x + 5y = 13, -3x - 3y = -6", "x = -1, y = 3",
+                              systemOfEquationsFunc)